Software to detect fraud in consumer phone cards tracks the number of metropolit

Question

Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 296 of the legitimate users originate calls from two or mo metropolitan areas in a single day. However, 30% of fraudulent users originate calls from two or more metropolitan areas in a single day. The proportion of fraudulent users is 0.0162%. If the same user originates calls from two or more metropolitan areas in a single day, what is the probability that the user is fraudulent? Round your answer to six decimal places (e.g. 98.765432)

Explanation / Answer

Answer :

P( fraudulent | originate call from metro cities) =p(fraudulent and originate call from 2 or 3 metro cities) / p(originating call from multiple metro cities) = 0.3 / 0.32 = 0.937500

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